Standard Factored and Vertex Form

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How can you identify the vertex of a quadratic function in vertex form?

Back

In vertex form f(x) = a(x - h)² + k, the vertex is the point (h, k).

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

How do you convert from vertex form to standard form?

Back

To convert from vertex form f(x) = a(x - h)² + k to standard form, expand the equation: f(x) = a(x² - 2hx + h²) + k.

Front

What is the significance of the 'a' value in the vertex form?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola.

Front

What is the y-intercept of a quadratic function in standard form?

Back

The y-intercept of a quadratic function in standard form f(x) = ax² + bx + c is the value of f(0), which equals c.

Front

What does it mean if the vertex of a parabola is a maximum?

Back

If the vertex is a maximum, the parabola opens downward, and the vertex represents the highest point on the graph.

Front

What does it mean if the vertex of a parabola is a minimum?

Back

If the vertex is a minimum, the parabola opens upward, and the vertex represents the lowest point on the graph.

Front

What is a parabola?

Back

A parabola is the graph of a quadratic function, which is a U-shaped curve that can open upward or downward.

Front

How do you find the axis of symmetry of a parabola?

Back

The axis of symmetry of a parabola in vertex form f(x) = a(x - h)² + k is the vertical line x = h.